Turnpike properties in nonlinear system identification
arXiv:2609.02071
2026
Dynamics
2 ideas extracted · analyzed Sep 3, 2026
What the math gives to ML
The paper offers a transferable turnpike mechanism for simulation-error training of nonlinear state-space models. Under reachability, incremental output stability, convex stage costs, and a suitable optimality condition, trajectories optimized from a fixed initial state approach the best trajectory obtained when the initial state is free. This supports shorter recurrent training windows and provides a quantitative prediction: if cumulative deviation is bounded independently of horizon, the average fixed-versus-free trajectory gap decays as O(1/N). The equivalence with strict dissipativity and value-function coercivity also suggests a trainable storage-function regularizer for neural state-space models.
Ideas from this paper
✗ Mechanism failed
2026
Attach a learned nonnegative storage function to a neural state-space model and penalize violations of a strict dissipativity inequality during rollout training. The resulting telescoping inequality limits cumulative output deviation and provides a monitor for whether long-horizon simulations are entering a stable turnpike regime.
Useful8/10
Difficulty6/10
Novelty6/10
✗ Mechanism failed
2026
Train a recurrent or neural state-space model on fixed-initial-state subsequences, but select the training horizon and burn-in from an empirically estimated turnpike bound instead of choosing them arbitrarily. If the cumulative discrepancy between fixed-initial-state and free-initial-state optima is bounded, the average discrepancy decreases as 1/N, allowing shorter windows while preserving the long-horizon optimum.
Useful8/10
Difficulty4/10
Novelty7/10